How do you show the group of digits that repeat in a repeating decimal? (1 point)
A. by printing them in italics
B. by underlining them
C. by putting a bar over them
D. by putting them in parentheses
C. by putting a bar over them
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7? (1 point)
A. up to six digits long
B. up to seven digits long
C. infinitely long
D. any finite length
B. up to seven digits long
To convert 0.264 to a rational number, you would set x equal to 0.264 and then multiply both sides of the equation by what number? (1 point)
A. 1,000
B. 999
C. 100
D. 10
A. 1,000
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
A. 99
B. 100
C. 999
D. 1,000
C. 999
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
127
Start Fraction 1 over 27 end fraction
2799
Start Fraction 27 over 99 end fraction
27100
Start Fraction 27 over 100 end fraction
311
B. Start Fraction 27 over 99 end fraction
The correct answer is C. by putting a bar over them.
To understand how to represent the repeating digits in a repeating decimal, let's first define what a repeating decimal is. A repeating decimal is a decimal number that has a pattern of digits that repeats endlessly. For example, the decimal representation of 1/3 is 0.333..., where the digit 3 repeats infinitely.
To express the repeating digits in a clear and standardized way, we use a bar notation. This notation involves placing a horizontal line, or a bar, over the repeating digit or group of digits. By doing so, we indicate that those digits repeat indefinitely.
For instance, if we have the repeating decimal 0.272727..., the repeating digit group is "27." To show this, we would write the number as 0.27 with a bar placed above the "27," like this: 0.27̅.
Therefore, the correct way to represent the repeating digits in a repeating decimal is by putting a bar over them, as indicated in option C.